New York State Democratic Party sources tell NBC News that Caroline Kennedy has expressed interest in the New York Senate seat being vacated by Hillary Clinton.

She is known to have discussed the upcoming vacancy with New York Gov. David Paterson, who will be appointing the next senator to serve the remaining two years in Clinton’s term once she becomes Secretary of State.

Appointing Caroline Kennedy to the seat once held by her uncle Robert would be a very popular choice politically for Paterson, who is under pressure to replace Clinton with a woman.

The Kennedy name on the ballot could help Paterson’s 2010 reelection chances. Paterson became governor after Eliot Spitzer was forced to resign during a prostitution scandal.

Caroline Kennedy would also have an advantage in being able to raise money for the very expensive New York Senate contest.

Other contenders — if Kennedy is not chosen — include be congress members Kirsten Gillibrand (from an Upstate district) and Carolyn Maloney (NYC), Nassau County Executive Thomas Suozzi and New York Attorney General Andrew Cuomo is also a possible contender.

Kennedy’s cousin — Robert Jr., an environmentalist, has taken himself out of contention